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A rectangle is presented. The length of a diagonal is marked. The sides of the rectangle are given in terms of expressions in x. The challenge is to determine the value of x. Solving the problem involves the use of Pythagoras’ theorem which then gives rise to a quadratic with quadratic coefficient greater than one. The quadratic can be solved by factorisation.

The ‘something in common’ is that in each example given x turns out to be 8. A subsequent challenge is to work out how all of the answers are the same.

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